Question

In a rectangle field of dimensions 50m ×30m a triangular park is constructed.If the dimensions of the park are 14m and 13 m . find the area of remaining field.

Answer 1

Let the third side of the triangle be x m
Area of the triangle =
$\sqrt{ \frac{13 + 14 + x}{2} } ( \frac{13 + 14 + x}{2} - 13)( \frac{13 + 14 + x}{2} - 14)( \frac{13 + 14 + x}{2} - x) \\ \sqrt{ \frac{17 + x}{2} } ( \frac{x + 1}{2} )( \frac{x - 1}{2} )( \frac{27 - x}{2} ) \\ \frac{ + - \sqrt{(17 + x)( {x}^{2} - 1)(27 - x) } }{4}$
Area of rectangle =50(30)=1500 m2
Area left =
$1500 - \frac{ + - \sqrt{(17 + x)( {x}^{2} - 1)(27 - x) } }{4} \\ \frac{6000 - { + - \sqrt{(17 + x)( {x}^{2} - 1)(27 - x) } }}{4} {m}^{2}$